Claudia’s family is buying a new cabinet for their home. The height of the cabinet is 5 ft., its length is 4 ft., and its volume is 60 ft^3 . They need to know the width of the cabinet to make sure that it will fit in the space where they want to put it. Using the volume formula, V=lwh , rearrange the formula to highlight the quantity of interest. Note that volume is represented with a capital V in the formula.

Question

w=__/__

Answer 1

To find the width \( w \) of the cabinet using the volume formula, we start with the formula:

\[ V = l \times w \times h \]

where:

• \( V \) is the volume,
• \( l \) is the length,
• \( w \) is the width, and
• \( h \) is the height.

We want to rearrange this formula to solve for \( w \). To do this, we can follow these steps:

1. Divide both sides of the equation by \( l \) and \( h \):

\[ w = \frac{V}{l \times h} \]

Now, substituting the known values into the equation, we have:

• \( V = 60 , \text{ft}^3 \)
• \( l = 4 , \text{ft} \)
• \( h = 5 , \text{ft} \)

So, the rearranged formula for \( w \) is:

\[ w = \frac{60}{4 \times 5} \]

Calculating the denominator:

\[ 4 \times 5 = 20 \]

Now substituting that back into the equation for \( w \):

\[ w = \frac{60}{20} = 3 , \text{ft} \]

Therefore, the width \( w \) of the cabinet is \( 3 , \text{ft} \).

In summary, the rearranged formula to find the width \( w \) is:

\[ w = \frac{V}{l \times h} \]